[EX02-206] The manager of Jerry’s Barber Shop recently asked his last 50 customers to punch a time card when they first arrived at the shop and to punch out right after they paid for their haircut.

He then used the data on the cards to measure how long it took Jerry and his barbers to cut hair and used that information to schedule their appointment intervals. The following times (in minutes)

were tabulated:

50 21 36 35 35 27 38 51 28 35 32 32 27 25 24 38 43 46 29 45 40 27 36 38 35 31 28 38 33 46 35 31 38 48 23 35 43 31 32 38 43 32 18 43 52 52 49 53 46 19

a. Construct a stem-and-leaf plot of these data.

b. Compute the mean, median, mode, range, midrange, variance, and standard deviation of the haircut service times.

c. Construct a 5-number summary table.

d. According to Chebyshev’s theorem, at least 75% of the haircut service times will fall between what two values? Is this true? Explain why or why not.

e. How far apart would you recommend that Jerry schedule his appointments to keep his shop operating at a comfortable pace?